Given the metric space (M,d) where M = RxR and d(x,y) = the Euclidean metric, what is the interior of the subset of M, QxQ?

I realize it is the empty set because there are points that lie in the open ball of any element of QxQ that are not actually in the set QxQ.

What I am struggling with is giving a formal, reasonable justification of why the interior is the empty set.

Any help or suggestions to get me thinking in a good direction would be greatly appreciated. Thank you so much, in advance!

To prove what Plato has said, try to prove that if are dense subsets of the topological spaces then is dense in under the product topology. Now since is dense in we know that is dense in . Similarly, is dense in and so given any for any neighborhood of there exists points of both and since the latter is a subset of it follows that . Since was arbitrary it follows that . And, as Plato pointed out we have that no interior point can be a boundary point, and so